Question $1(25$ points$)$

$8-1.($Production problem$)$ Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of $300$ of each cabinet per week $($or $60$ cabinets per day$).$ Owner Bob Winkler would like to determine a product mix to maximize his daily revenue.

a$.$ Formulate as an LP problem.

b$.$ Solve using an LP software program or spreadsheet

Aftereconsidering these calculations, the product mix to maximizes daily revenue is to produce:

$60$ French Provincial cabinets $(x_1)$ per day and

$90$ Danish Modern cabinets $(x_2)$ per day

True

False